On the topology of families of isolated singularities

2014/11/27 by Neto, Aurelio Menegon
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1411.7609

openalex publication_date 2014/11/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the topology of analytic families of n-dimensional complex hypersurfaces having an isolated singularity at the origin. We prove that such a family is μ-constant if and only if it admits an uniform Milnor radius, which happens if and only if it has constant embedded topological type. In particular, this solves the μ-constant problem, formulated by D.T. Lê and C.P. Ramanujam in 1976.

Citations

• Uniform radius and regular stratifications

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